Sorry to see nobody has responded to you since you posted last June. :-(
Are the paper records copies of the official records provided him by the US military, or other non-official items?
"Artifact, privately held" is certainly a generic enough source type that you could use for pretty much any family heirloom, including military records. There's also "Miscellaneous Documents, Unpublished." Again, it's a generic item, though it also references film data and roll number in the template for some reason that I can't fathom.
If you're talking about his official service file there are a couple of them, though they point to copies of the filmed records. This is what you would get if you sent a request to NARA for copies.
Good luck! It's hard to pick a pre-existing template sometimes. Right now, I'm wrestling with records for the Azores (small Portuguese islands in the mid-Atlantic). They have filmed church records. But, there are no pre-existing templates that I like so I've decided to make one up, and then share it with others in the custom source templates page. But, making one just the way I like it is like pulling teeth. :-)